Long-Term Memory, Simulated Qubits, Physical Qubits - Brain Theory from a Circuits and Systems Perspective - page 63

Other circuits involving an enabled AND gate could be used in place of the XOR
and could provide the same sort of function without a need for coordinated timing
(devising this circuit is left as an exercise). Hybrid arrangements are not as complex as
they look and are quite useful whenever a specific pulse burst is required. Recursive
neurons and multivibrators bring to mind similar structures with qubit-like properties.

Simulated Qubits

Recursive circuits as above have certain qubit-like properties, which, by the way, is
why they are especially interesting. Advantages of qubit-like properties in a
biological brain are, they can hold true and false simultaneously, releasing a logic
value with a given probability when the circuit receives a read pulse. Moreover, a
recursive circuit can be made to give a controlled toggle, which is a most useful
type of neural operation.

Toggling works as follows: If probabilities are adjusted to give a true value with
100 % probability, a toggle would change (flip) this to false with 100 % probability.
Similarly, false could flip to true. Controlled toggle circuits are termed controlled
because they will flip only when other qubits in the system are true. They are quite
useful for explaining mental arithmetic and other brain functions, so much so that
they have been proposed to underlie gifted mental savants [ 3 ].
Recursive multivibrating neurons are easily converted into simulated qubits.
Simulated qubits are discussed below and subsequently they will be compared with
the qubits of quantum mechanics.
Recursive neurons as above, once triggered, sustain a sequence of pulses with
similar amplitudes. Each pulse tends to have a brief width ( ) but the separation

between pulses can vary; the frequency of pulses within a given neuron may range
from a few hundred hertz to zero frequency, depending on neuronal delay
parameters.
The general form of a simulated qubit is diagramed in Fig. 4.5 . Unit A contains
OR gate recursive circuitry as introduced above.
Note that the trigger to Unit A involves a weak synapse S1 to produce a single
pulse, Trigger(1). To ensure that the recycling pulse remains a single pulse, weak
synapse S2 maintains a single pulse and serves to produce Pulse(2) which closes the
loop. The waveform emerging on the right at point x will be sampled to establish
either true or false. If the waveform is at a high level when sampled, the output
will be true. If the waveform is at low level when sampled, the output will be false.
This circuit provides true or false with a probability that depends on the frequency
of multivibration.
To increase the computational possibilities, the relative phase of the output
signal may be adjusted using Delay

τ

φ . This is referred to as phase shifting and its

uses are explored in a later chapter.
The lowest frequency f 0 of pulses is defined to be state “zero” which can be
related to false. The highest frequency f 1 is defined to be state “one” which can